CMA-676 [a conjugate composed of an engineered human anti-CD33 antibody (hP67.6) linked to a potent antitumor antibiotic, calicheamicin] provides a new method of drug delivery by utilizing a monoclonal antibody to target leukemic cells. Since CD33 is expressed on leukemic cells in 90% of cases of AML, but is not expressed in non-hematopoietic tissues, calicheamicin is targeted selectively to the leukemic cells. Although 50-70% of patients with AML achieve CR as a result of initial treatment, approximately 80% ultimately relapse, and the cure rate for relapsed patients is extremely low. This is a three part, open-label, single-arm, multicycle, multicenter outpatient study with a study drug infusion observation period. The study will examine the effects of CMA-676 given intravenously to patients with CD33+ AML in first relapse. The primary objectives of this study are to assess efficacy in terms of the number of patients attaining a complete remission (CR) and to assess the safety of CMA-676. The study will also assess the duration of CRs and morphologic remissions, the pharmacokinetic (PK) properties of CMA-676 and possible predictors of response to CMA-676.